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Radial Flow Reaction Turbines (continued)

Vector diagrams.

First find a₁ for shockless entry.

Strategy: Use vector plot at entrance to find tan a₁ .

At the entrance to the turbine: Q = 2 π r₁ b₁ V_r1 So V_r1 = Q / (2 π r₁ b₁ )

and tan β₁ = V_r1 / W_t1 So W_t1 = V_r1 / tan β₁ = Q / (2 π r₁ b₁ )( tan β₁ )

Now tan a₁ = V_r1 / ( r₁ ω + W_t1 ) The result: a₁ = tan^˗1 (V_r1 / ( r₁ ω + W_t1 ) (result)

For the given data: V_r1 = 10.61 ft/sec, W_t1 = 6.125 ft/sec

Here w = 2 π (rad/rev) N (rev/min) / 60 (sec/min) = 6.7 rad/sec r₁w = 33.5 ft/sec

and a₁ = tan^˗1 [10.61/ (33.5 + 6.125)] = 15^o (result)

Calculate tangential component of absolute velocity of fluid at the entrance to the turbine.

Use the vector plot at the entrance to the turbine shown above.

V_t1 = ˗ (r₁ ω + W_t1) = ˗ ( 33.5 + 6.125) = ˗ 39.63 ft/sec